Smooth finitely computable functions are affine, or why quantum systems cause waves
Vladimir Anashin · Doklady Mathematics · 2015
Abstract—It is shown that the class of all C 2-smooth real functions that can be computed (in a new, but natural sense precisely defined below) on Mealy machines (letter-to-letter transducers or, briefly, transducers) consists of affine functions only. Moreover, it turns out that all these functions can be naturally associated with wave functions of particles. Accordingly, this work can be regarded as a mathematical reasoning that the wave properties of quantum systems are caused by the discreteness of matter and causality, since transducers are a mathematical formalization of the law of causality.